The Non-Intercept Linear Regression Method Sigit Haryadi Institut Teknologi Bandung
[email protected]
Abstract- Non-Intercept Linear regression is the measurement of the linear relationship between two random variables having complete interdependence, meaning that if one variable does not exist, then another variable is should absent. In other words. The regression equation can be written mathematically Y = bX or h(w) = w x , where the level of correlation between two random variables tested and simultaneous states the level of confidence of the resulting regression equation will be estimated by a coefficient called Haryadi Index (HI), which I compiled in April 2016. The advantage of this method is to remain accurate regardless of sample size, and more importantly to avoid mistakes inferring data on events where regression equations should be past the origin point (0,0), but we are forced to produce a regression equation that passes through the non-origin point (0, not 0) and (not 0, 0), as a result, have used the existing formula. The disadvantage of this method is not well known, leading to unavailability of a calculator or software to calculate the correlation index quickly. Keyword: Linear regression; Non-intercept; Haryadi index; accurate regardless of sample size; past the origin point
1. Background At the time of making a regression and a forecasting on a complex data, I usually use Fourier series [4], but on the simple issue, I often use a simple linear regression Y = a + bX, or an univariate regression h(w) = w0 + w1 x or the multivariate regression h(w) = w0 + w1x1 + w2x2 + …+ wn xn. Unfortunately, linear regression using existing formulas often frustrates us. For example, we will calculate the correlation between the amount of data transmitted by an internet network as a function of internet data rate, it is clear that we hope that the linear regression must pass through the origin point (0,0), meaning that there is no internet transmitted when the internet speed is zero. But unfortunately, due to using the existing formula, we forced to accept a regression equation that has an intercept value, meaning the regression does not pass through the origin point, that means there is an internet data transmitted when the internet speed is equal to zero, on another occasion we forced to conclude that there is the minus internet traffic when internet speed is zero. This disappointment forced me to look for a regression method that did not have an intercept value, and finally in August 2016 [2, 3], I discovered that the Haryadi Index I found in April 2016 [1], initially only aimed at measuring the level of competition in a telecommunications industry, replacing the existing method, the Herfindahl-Hirschman Index, can also be used for non-intercept linear regression problem.
2. Definition Non-Intercept Linear regression is the measurement of the linear relationship between two random variables having complete interdependence, meaning that if one variable does not exist, then another variable is also absent. In other words. The regression equation can be written mathematically Y = bX or h(w) = wx , where the level of correlation between two random variables tested, and simultaneous states the level of confidence of the regression equation will be estimated by a coefficient called Index Haryadi (HI), which I invented in April 2016.
1
1
=
∑
+∑
∑
−
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Si = the share of the regression coefficient or slope = =
,
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, ∑ -
ℎ ℎ ℎ ℎ
!ℎ !ℎ
"#$ ! % &% '' !( )*# !( ' + = , "#$ ! % &% '' !( )*# !( ' h/w1 = -2
3. Determining Confidence Level of the Regression Equation Determination of the confidence level of the Hypothetical Regression Equation is done by referring to table 1 as follows TABLE 1. Confidence Level of the Regression Equation CORRELATION INDEX HI = 1.00 0.95 ≤ HI < 1.00 0.75 ≤ HI < 0.95 0.60 ≤ HI < 0.75 0.50 ≤ HI < 0.60 HI < 0.50 HI ≤ {(N-1)/2N}
LEVEL OF CONFIDENCE OF THE REGRESSION Perfect Almost Perfect Strong Medium Weak Almost Wrong at All Wrong at all
4. Calculation Examples
4.1.Case 1.a. Use the following measurement data to create a linear regression equation without intercept and estimate the correlation index and determine the level of confidence of the regression equation. No 1 2 3 4 5 6
X
Y
104 103 98 103 92 108
211 207 200 204 180 210
Answer: No 1 2 3 4 5 6
X
Y
b = Y/X
Si = bi/Ʃbi
104 211 2.03 0.1696 103 207 2.01 0.1680 98 200 2.04 0.1706 103 204 1.98 0.1656 92 180 1.96 0.1636 108 210 1.94 0.1626 TOTAL = 11.96 1.000 Average = 1.99 0.1667 Correlation Index = 0.998 Regression equation Y = 1.99X is Almost Perfect
Explanation:
2
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The hypothesis of the regression equation is Y = 1.99 X, because b = the average of Y/X = 1.99
•
Because the sample size of the data = 6, then the correlation index = HI(6) = 1/[6{S12 + S22 + S32 + S42 + S52 + S62 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5-S1)2 + (S6-S1)2 + (S3S2)2 + (S4-S2)2 + (S5-S2)2 + (S6-S2)2 + (S4-S3)2 + (S5-S3)2 + (S6-S3)2 + (S5-S4)2 + (S6-S4)2 + (S6-S5)2}], or in excel written as follows: 1/(6*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + S6^2 + (S2-S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S5-S1)^2 + (S6-S1)^2 + (S3-S2)^2 + (S4S2)^2 + (S5-S2)^2 + (S6-S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S6-S3)^2 + (S5-S4)^2 + (S6S4)^2 + (S6-S5)^2)) = 1/(6*(0.1696^2 + 0.1680^2 + 0.1706^2 + 0.1656^2 + 0.1636^2 + 0.1626^2 + (0.1680-0.1696)^2 + (0.1706-0.1696)^2 + (0.1656-0.1696)^2 + (0.16360.1696)^2 + (0.1626-0.1696)^2 + (0.1706-0.1680)^2 + (0.1656-0.1680)^2 + (0.16360.1680)^2 + (0.1626-0.1680)^2 + (0.1656-0.1706)^2 + (0.1636-0.1706)^2 + (0.16260.1706)^2 + (0.1636-0.1656)^2 + (0.1626-0.1656)^2 + (0.1636-0.1626)^2)) = 0.998
•
Conclusion: From the measurement data given, the regression equation is Y = 1.99 X is having a correlation index between Y and X of 99.8%, which states that the confidence level of the regression is almost perfect.
4.2.Case 1.b. Use the following measurement data to create a linear regression equation without intercept and estimate the correlation index and determine the level of confidence of the regression equation. No 1 2 3 4 5 6
X
Y
104 103 98 103 92 108
200 100 300 50 250 350
Answer: No
X
Y
b = Y/X
Si = bi/Ʃbi
104 200 1.92 0.1551 103 100 0.97 0.0783 98 300 3.06 0.2469 103 50 0.49 0.0392 92 250 2.72 0.2192 108 350 3.24 0.2614 TOTAL = 12.40 1.000 Average = 2.07 0.1667 Correlation Index = 0.360 Regression equation Y = 2.07X is Almost Wrong at All 1 2 3 4 5 6
Explanation:
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The hypothesis of the regression equation is Y = 2.07 X, because b = the average of Y/X = 2.07
3
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Because the sample size of the data = 6, then the correlation index = HI(6) = 1/[6{S12 + S22 + S32 + S42 + S52 + S62 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5-S1)2 + (S6-S1)2 + (S3S2)2 + (S4-S2)2 + (S5-S2)2 + (S6-S2)2 + (S4-S3)2 + (S5-S3)2 + (S6-S3)2 + (S5-S4)2 + (S6-S4)2 + (S6-S5)2}], or in excel written as follows: 1/(6*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + S6^2 + (S2-S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S5-S1)^2 + (S6-S1)^2 + (S3-S2)^2 + (S4S2)^2 + (S5-S2)^2 + (S6-S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S6-S3)^2 + (S5-S4)^2 + (S6S4)^2 + (S6-S5)^2)) = 1/(6*(0.1551^2 + 0.0783^2 + 0.2469^2 + 0.0392^2 + 0.2192^2 + 0.2614^2 + (0.0783-0.1551)^2 + (0.2469-0.1551)^2 + (0.0392-0.1551)^2 + (0.21920.1551)^2 + (0.2614-0.1551)^2 + (0.2469-0.0783)^2 + (0.0392-0.0783)^2 + (0.21920.0783)^2 + (0.2614-0.0783)^2 + (0.0392-0.2469)^2 + (0.2192-0.2469)^2 + (0.26140.2469)^2 + (0.2192-0.0392)^2 + (0.2614-0.0392)^2 + (0.2192-0.2614)^2)) = 0.36
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Conclusion: From the measurement data given, the regression equation is Y = 2.07 X is having a correlation index between Y and X of 36 %, which states that the confidence level of the regression is almost wrong at all.
4.3.Case2.a. Use the following measurement data to create a linear regression equation without intercept and estimate the correlation index and determine the level of confidence of the regression equation. No
h
x
1 2 3
7 9 13
35 36 39
Answer: No
h
x
w = h/x
Si = wi/Ʃwi
7 35 1 5.00 0.4167 9 36 2 4.00 0.3333 13 39 3 3.00 0.2500 TOTAL = 12.00 1.0000 Average = 4.00 Correlation Index = 0.857 Regression equation h(w) = 4.00x is Strong
Explanation:
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The hypothesis of the regression equation is h(w) = 4.00 x, because w = the average of h/x = 4.00 Because the sample size of the data = 3, then the correlation index = HI(3) = 1/[3{S12 + S22 + S32 + (S2-S1)2 + (S3-S1)2 + (S3-S2)2}], or in excel written as follows:1/(3*(S1^2 + S2^2 + S3^2 + (S2-S1)^2 + (S3-S1)^2 + (S3-S2)^2)) = 1/(3*(0.4167^2 + 0.3333^2 + 0.2500^2 + (0.3333-0.4167)^2 + (0.2500-0.4167)^2 + (0.2500-0.3333)^2)) = 0.857
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Conclusion: From the measurement data given, the regression equation is h = 4.00 X is having a correlation index between h(w) and x of 85.7 %, which states that the confidence level of the regression is strong.
4.4.Case 2.b. Use the following measurement data to create a linear regression equation without intercept and estimate the correlation index and determine the level of confidence of the regression equation. No
h
x
1 2 3
7 9 13
30 18 23
Answer: No
h
x
w = h/x
Si = wi/Ʃwi
7 30 1 4.29 0.5321 9 18 2 2.00 0.2483 13 23 3 1.77 0.2196 TOTAL = 8.05 1.0000 Average = 2.68 Correlation Index = 0.583 Regression equation h(w) = 2.68 x is Weak
Explanation:
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•
The hypothesis of the regression equation is h(w) = 2.68 x, because w = the average of h/x = 2.68 Because the sample size of the data = 3, then the correlation index = HI(3) = 1/[3{S12 + S22 + S32 + (S2-S1)2 + (S3-S1)2 + (S3-S2)2}], or in excel written as follows: 1/(3*(S1^2 + S2^2 + S3^2 + (S2-S1)^2 + (S3-S1)^2 + (S3-S2)^2)) = 1/(3*(0.5321^2 + 0.2483^2 + 0.2196^2 + (0.2483-0.5321)^2 + (0.2196-0.5321)^2 + (0.21960.2483)^2)) = 0.582. Conclusion: From the measurement data given, the regression equation is h = 2.68 x is having a correlation index between h(w) and x of 58.2 %, which states that the confidence level of the regression is weak.
5. Examples of correlation formula: a) Sample size is 2, then HI(2) = 1/[2{S12 + S22 + (S2-S1)2}] b) Sample size is 3, then HI(3) = 1/[3{S12 + S22 + S32 + (S2-S1)2 + (S3-S1)2 + (S3-S2)2}] c) Sample size is 4, then HI(4) = 1/[4{S12 + S22 + S32 + S42 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S3-S2)2 + (S4-S2)2 + (S4-S3)2}] d) Sample size is 5, then HI(5) = 1/[5{S12 + S22 + S32 + S42 + S52 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5S1)2 + (S3-S2)2 + (S4-S2)2 + (S5-S2)2 + (S4-S3)2 + (S5-S3)2 + (S5-S4)2}] e) Sample size is 6, then HI(6) = 1/[6{S12 + S22 + S32 + S42 + S52 + S62 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5-S1)2 + (S6-S1)2 + (S3-S2)2 + (S4-S2)2 + (S5-S2)2 + (S6-S2)2 + (S4-S3)2 + (S5-S3)2 + (S6-S3)2 + (S5S4)2 + (S6-S4)2 + (S6-S5)2}]
5
f) Sample size is 7, then HI(7) = 1/[7{S12 + S22 + S32 + S42 + S52 + S62 + S72 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5-S1)2 + (S6-S1)2 + (S7-S1)2 + (S3-S2)2 + (S4-S2)2 + (S5-S2)2 + (S6-S2)2 + (S7-S2)2 + (S4-S3)2 + (S5-S3)2 + (S6-S3)2 + (S7-S3)2 + (S5-S4)2 + (S6-S4)2+ (S7-S4)2 + (S6-S5)2 + (S7-S5)2 + (S7-S6)2}] g) Sample size is 8, then HI(8) = 1/[8{S12 + S22 + S32 + S42 + S52 + S62 + S72 + S82 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5-S1)2 + (S6-S1)2 + (S7-S1)2 + (S8-S1)2 + (S3-S2)2 + (S4-S2)2 + (S5-S2)2 + (S6-S2)2 + (S7S2)2 + (S8-S2)2 + (S4-S3)2 + (S5-S3)2 + (S6-S3)2 + (S7-S3)2 + (S8-S3)2 + (S5-S4)2 + (S6-S4)2 + (S7-S4)2 + (S8-S4)2 + (S6-S5)2 + (S7-S5)2 + (S8-S5)2 + (S7-S6)2 + (S8-S6)2 + (S8-S7)2}] h) Sample size is 9, then HI(9) = 1/[9{S12 + S22 + S32 + S42 + S52 + S62 + S72 + S82 + S92 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5-S1)2 + (S6-S1)2 + (S7-S1)2 + (S8-S1)2 + (S9-S1)2 + (S3-S2)2 + (S4-S2)2 + (S5-S2)2 + (S6-S2)2 + (S7-S2)2 + (S8-S2)2 + (S9-S2)2 + (S4-S3)2 + (S5-S3)2 + (S6-S3)2 + (S7-S3)2 + (S8-S3)2 + (S9S3)2 + (S5-S4)2 + (S6-S4)2 + (S7-S4)2 + (S8-S4)2 + (S9-S4)2 + (S6-S5)2 + (S7-S5)2 + (S8-S5)2 + (S9-S5)2 + (S7-S6)2 + (S8-S6)2 + (S9-S6)2 + (S8-S7)2 + (S9-S7)2 + (S9-S8)2}] i)
Sample size is 10, then HI(10) = 1/[10{S12 + S22 + S32 + S42 + S52 + S62 + S72 + S82 + S92 + S102 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5-S1)2 + (S6-S1)2 + (S7-S1)2 + (S8-S1)2 + (S9-S1)2 + (S10-S1)2 + (S3S2)2 + (S4-S2)2 + (S5-S2)2 + (S6-S2)2 + (S7-S2)2 + (S8-S2)2 + (S9-S2)2 + (S10-S2)2 + (S4-S3)2 + (S5-S3)2 + (S6-S3)2 + (S7-S3)2 + (S8-S3)2 + (S9-S3)2 + (S1o-S3)2 + (S5-S4)2 + (S6-S4)2 + (S7-S4)2 + (S8-S4)2 + (S9S4)2 + (S10-S4)2 + (S6-S5)2 + (S7-S5)2 + (S8-S5)2 + (S9-S5)2 + (S10-S5)2 + (S7-S6)2 + (S8-S6)2 + (S9-S6)2 + (S10-S6)2 + (S8-S7)2 + (S9-S7)2 + (S10-S7)2 + (S9-S8)2 + (S10-S8)2 + (S10-S9)2}]
j)
Sample size is 11, then HI(11) = 1/[11{S12 + S22 + S32 + S42 + S52 + S62 + S72 + S82 + S92 + S102 + S112 + (S2-S1)2 + (S3-S1)2 + (S4-S1)2 + (S5-S1)2 + (S6-S1)2 + (S7-S1)2 + (S8-S1)2 + (S9-S1)2 + (S10-S1)2 + (S11-S1)2 + (S3-S2)2 + (S4-S2)2 + (S5-S2)2 + (S6-S2)2 + (S7-S2)2 + (S8-S2)2 + (S9-S2)2 + (S10-S2)2 + (S11S2)2 + (S4-S3)2 + (S5-S3)2 + (S6-S3)2 + (S7-S3)2 + (S8-S3)2 + (S9-S3)2 + (S10-S3)2 + (S11-S3)2 + (S5-S4)2 + (S6-S4)2 + (S7-S4)2 + (S8-S4)2 + (S9-S4)2 + (S10-S4)2 + (S11-S4)2 + (S6-S5)2 + (S7-S5)2 + (S8-S5)2 + (S9S5)2 + (S10-S5)2 + (S11-S5)2 + (S7-S6)2 + (S8-S6)2 + (S9-S6)2 + (S10-S6)2 + (S11-S6)2 + (S8-S7)2 + (S9-S7)2 + (S10-S7)2 + (S11-S7)2 + (S9-S8)2 + (S10-S8)2 + (S11-S8)2 + (S10-S9)2 + (S11-S9)2 + (S11-S10)2}]
And so on. Correlation formula in Excel is written as follows: a) HI(2) =1/(2*(S1^2 + S2^2 + (S2-S1)^2)) b) HI(3) = 1/(3*(S1^2 + S2^2 + S3^2 + (S2-S1)^2 + (S3-S1)^2 + (S3-S2)^2)) c) HI(4) = 1/(4*(S1^2 + S2^2 + S3^2 + S4^2 + (S2-S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S3-S2)^2 + (S4S2)^2 + (S4-S3)^2)) d) HI(5) = 1/(5*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + (S2-S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S5-S1)^2 + (S3-S2)^2 + (S4-S2)^2 + (S5-S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S5-S4)^2)) e) HI(6) = 1/(6*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + S6^2 + (S2-S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S5-
6
S1)^2 + (S6-S1)^2 + (S3-S2)^2 + (S4-S2)^2 + (S5-S2)^2 + (S6-S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S6S3)^2 + (S5-S4)^2 + (S6-S4)^2 + (S6-S5)^2)) f) HI(7) = 1/(7*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + S6^2 + S7^2 + (S2-S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S5-S1)^2 + (S6-S1)^2 + (S7-S1)^2 + (S3-S2)^2 + (S4-S2)^2 + (S5-S2)^2 + (S6-S2)^2 + (S7-S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S6-S3)^2 + (S7-S3)^2 + (S5-S4)^2 + (S6-S4)^2 + (S7-S4)^2 + (S6-S5)^2 + (S7-S5)^2 + (S7-S6)^2)) g) HI(8) = 1/(8*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + S6^2 + S7^2 + S8^2 + (S2-S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S5-S1)^2 + (S6-S1)^2 + (S7-S1)^2 + (S8-S1)^2 + (S3-S2)^2 + (S4-S2)^2 + (S5-S2)^2 + (S6-S2)^2 + (S7-S2)^2 + (S8-S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S6-S3)^2 + (S7-S3)^2 + (S8-S3)^2 + (S5-S4)^2 + (S6-S4)^2 + (S7-S4)^2 + (S8-S4)^2 + (S6-S5)^2 + (S7-S5)^2 + (S8-S5)^2 + (S7-S6)^2 + (S8-S6)^2 + (S8-S7)^2)) h) HI(9) = 1/(9*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + S6^2 + S7^2 + S8^2 + S9^2 + (S2-S1)^2 + (S3S1)^2 + (S4-S1)^2 + (S5-S1)^2 + (S6-S1)^2 + (S7-S1)^2 + (S8-S1)^2 + (S9-S1)^2 + (S3-S2)^2 + (S4S2)^2 + (S5-S2)^2 + (S6-S2)^2 + (S7-S2)^2 + (S8-S2)^2 + (S9-S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S6S3)^2 + (S7-S3)^2 + (S8-S3)^2 + (S9-S3)^2 + (S5-S4)^2 + (S6-S4)^2 + (S7-S4)^2 + (S8-S4)^2 + (S9S4)^2 + (S6-S5)^2 + (S7-S5)^2 + (S8-S5)^2 + (S9-S5)^2 + (S7-S6)^2 + (S8-S6)^2 + (S9-S6)^2 + (S8S7)^2 + (S9-S7)^2 + (S9-S8)^2)) i)
HI(10) = 1/(10*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + S6^2 + S7^2 + S8^2 + S9^2 + S10^2 + (S2S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S5-S1)^2 + (S6-S1)^2 + (S7-S1)^2 + (S8-S1)^2 + (S9-S1)^2 + (S10S1)^2 + (S3-S2)^2 + (S4-S2)^2 + (S5-S2)^2 + (S6-S2)^2 + (S7-S2)^2 + (S8-S2)^2 + (S9-S2)^2 + (S10S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S6-S3)^2 + (S7-S3)^2 + (S8-S3)^2 + (S9-S3)^2 + (S10-S3)^2 + (S5S4)^2 + (S6-S4)^2 + (S7-S4)^2 + (S8-S4)^2 + (S9-S4)^2 + (S10-S4)^2 + (S6-S5)^2 + (S7-S5)^2 + (S8S5)^2 + (S9-S5)^2 + (S10-S5)^2 + (S7-S6)^2 + (S8-S6)^2 + (S9-S6)^2 + (S10-S6)^2 + (S8-S7)^2 + (S9S7)^2 + (S10-S7)^2 + (S9-S8)^2 + (S10-S8)^2 + (S10-S9)^2))
j)
HI(11) = 1/(11*(S1^2 + S2^2 + S3^2 + S4^2 + S5^2 + S6^2 + S7^2 + S8^2 + S9^2 + S10^2 + S11^2 + (S2-S1)^2 + (S3-S1)^2 + (S4-S1)^2 + (S5-S1)^2 + (S6-S1)^2 + (S7-S1)^2 + (S8-S1)^2 + (S9-S1)^2 + (S10-S1)^2 + (S11-S1)^2 + (S3-S2)^2 + (S4-S2)^2 + (S5-S2)^2 + (S6-S2)^2 + (S7-S2)^2 + (S8-S2)^2 + (S9-S2)^2 + (S10-S2)^2 + (S11-S2)^2 + (S4-S3)^2 + (S5-S3)^2 + (S6-S3)^2 + (S7-S3)^2 + (S8-S3)^2 + (S9-S3)^2 + (S10-S3)^2 + (S11-S3)^2 + (S5-S4)^2 + (S6-S4)^2 + (S7-S4)^2 + (S8-S4)^2 + (S9-S4)^2 + (S10-S4)^2 + (S11-S4)^2 + (S6-S5)^2 + (S7-S5)^2 + (S8-S5)^2 + (S9-S5)^2 + (S10-S5)^2 + (S11-S5)^2 + (S7-S6)^2 + (S8-S6)^2 + (S9-S6)^2 + (S10-S6)^2 + (S11-S6)^2 + (S8-S7)^2 + (S9-S7)^2 + (S10-S7)^2 + (S11-S7)^2 + (S9-S8)^2 + (S10-S8)^2 + (S11-S8)^2 + (S10-S9)^2 + (S11-S9)^2 + (S11-S10)^2))
k) And so on.
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Reference 1. Sigit Haryadi, "Haryadi Index and Its Applications in Science of Law, Sociology, Economics, Statistics, and Telecommunications," Jakarta, Indonesia: Elex Media Komputindo, pp. 10-20, 2017. Available in: https://www.getscoop.com/books/haryadi-index-and-its-applications-in-science-oflaw-sociology-economics-statistics-and-telecommunication 2. Nie-Levin Kusuma Adiatma and Sigit Haryadi, “Comparison of the Haryadi Index with Existing Method in Competition, Equality, Fairness, and Correlation Level Calculation Case Study: Telecommunication Industry,” Lombok, Indonesia, The 11th International Conference on Telecommunication Systems, Services, and Applications, At Lombok, Indonesia, In press to IEEExplore. Before editing paper available in https://www.researchgate.net/publication/320728316_Comparison_of_the_Haryadi_I ndex_with_Existing_Method_in_Competition_Equality_Fairness_and_Correlation_L evel_Calculation_Case_Study_Telecommunication_Industry 3. Sigit Haryadi, “The Equality Correlation Method a Notebook of Sigit Haryadi Institut Teknologi Bandung,” Unpublished article / Notebook, DOI: 10.13140/RG.2.2.10443.80169. Available in : https://www.researchgate.net/publication/317379400_The_Equality_Correlation_Met hod_A_Notebook_of_Sigit_Haryadi_Institut_Teknologi_Bandung 4. Dwina Fitriyandini Siswanto and Sigit Haryadi, “Broadband user demand forecasting in Indonesia based on Fourier analysis, ” Proceeding of 2015 1st International Conference on Wireless and Telematics, ICWT 2015, IEEExplore Article number 7449237, DOI: 10.1109/ICWT.2015.7449237.
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